Implementation of BVD (boundary variation diminishing) algorithm in simulations of compressible multiphase flows

TL;DR

This paper introduces a novel MUSCL-THINC-BVD scheme for simulating compressible multiphase flows, effectively capturing sharp interfaces and reducing numerical dissipation in the five-equation model.

Contribution

The paper develops a new reconstruction scheme combining MUSCL and THINC within the BVD principle for improved interface capturing in multiphase flow simulations.

Findings

Accurately captures sharp material interfaces.

Reduces numerical dissipation in simulations.

Improves solution quality in benchmark tests.

Abstract

We present in this work a new reconstruction scheme, so-called MUSCL-THINC-BVD scheme, to solve the five-equation model for interfacial two phase flows. This scheme employs the traditional shock capturing MUSCL (Monotone Upstream-centered Schemes for Conservation Law) scheme as well as the interface sharpening THINC (Tangent of Hyperbola for INterface Capturing) scheme as two building-blocks of spatial reconstruction using the BVD (boundary variation diminishing) principle that minimizes the variations (jumps) of the reconstructed variables at cell boundaries, and thus effectively reduces the numerical dissipations in numerical solutions. The MUSCL-THINC-BVD scheme is implemented to all state variables and volume fraction, which realizes the consistency among volume fraction and other physical variables. Benchmark tests are carried out to verify the capability of the present method in capturing the material interface as a well-defined sharp jump in volume fraction, as well as significant improvement in solution quality. The proposed scheme is a simple and effective method of practical significance for simulating compressible interfacial multiphase flows.